x+(100-2/3x)+(2/3x+20)=180

Solution for x+(100-2/3x)+(2/3x+20)=180 equation:

x+(100-2/3x)+(2/3x+20)=180

We move all terms to the left:

x+(100-2/3x)+(2/3x+20)-(180)=0


Domain of the equation: 3x)!=0

x!=0/1

x!=0

x∈R



Domain of the equation: 3x+20)!=0

x∈R


We add all the numbers together, and all the variables

x+(-2/3x+100)+(2/3x+20)-180=0

We get rid of parentheses

x-2/3x+2/3x+100+20-180=0

We multiply all the terms by the denominator


x*3x+100*3x+20*3x-180*3x-2+2=0

We add all the numbers together, and all the variables

x*3x+100*3x+20*3x-180*3x=0

Wy multiply elements

3x^2+300x+60x-540x=0

We add all the numbers together, and all the variables

3x^2-180x=0

a = 3; b = -180; c = 0;
Δ = b2-4ac
Δ = -1802-4·3·0
Δ = 32400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{32400}=180$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-180)-180}{2*3}=\frac{0}{6}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-180)+180}{2*3}=\frac{360}{6}
=60
$